10 Large Current Radiators: Problems, Analysis, and Design

When Prof. Henning F. Harmuth suggested using nonsinusoidal waves for radar and radio communication [1,2], he quite logically raised the problem of a special radiator for propagating (in current terminology) ultrawideband (UWB) pulse electromagnetic fields, and he suggested using “large current radiators” (LCRs) [3–5].

The LCR differs from well-known classical electric dipoles and magnetic loop radiators shown in Figure 10.1. Considering the substantial differences, it is suggested to designate the LCRs as a special class of electromagnetic radiators. Distinct from the loop antenna, the LCR radiates in a more effective dipole mode like the Hertzian electric dipole. However, in contrast to the electric dipole, the LCR has low resistance permitting the excitation with a large current at a low driving voltage like the magnetic dipole, which increases the radiation efficiency. Thus, based on Harmuth’s reasoning, the LCR should make an effective radiator.

Some researchers including Malek G.M. Hussain of the University of Kuwait [7], Robert Fleming of AetherWire and Location, N.J. Mohamed of Kuwait University, Safat, Kuwait [8], and the authors have collaborated with their colleagues for developing an LCR that is more effective when compared with other radiators for UWB signals.

The next sections consider the physical and technical problems arising during LCR design, as well as some ways to overcome them. They also provide the results of theoretical and experimental investigations to illustrate the concepts for improved LCR designs.

10.2 Basic LCR Antenna Principles

We start by writing the equations for electric and magnetic field strengths, $\vec{E}$ $\vec{E}$ and $\vec{H}$ $\vec{H}$ respectively, radiated by a small dipole in the far zone.

\vec{E} = \frac{1}{r} \frac{Z_{0} ℓ}{4 π c} \frac{d I_{r a d}}{d t} \frac{\vec{r} \times (\vec{r} \times \vec{ℓ})}{ℓ \cdot r^{2}} (10.1)

$\vec{E} = \frac{1}{r} \frac{Z_{0} ℓ}{4 π c} \frac{d I_{r a d}}{d t} \frac{\vec{r} \times (\vec{r} \times \vec{ℓ})}{ℓ \cdot r^{2}} (10.1)$

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FIGURE 10.1
The LCR combines dipole radiation mode and low resistance.

\vec{H} = \frac{1}{r} \frac{ℓ}{4 π c} \frac{d I_{r a d}}{d t} \frac{\vec{ℓ} \times \vec{r}}{ℓ \cdot r} (10.2)

$\vec{H} = \frac{1}{r} \frac{ℓ}{4 π c} \frac{d I_{r a d}}{d t} \frac{\vec{ℓ} \times \vec{r}}{ℓ \cdot r} (10.2)$

where I_rad is the radiator current, ℓ is the dipole length, $z_{0} = \sqrt{μ_{0} / ε_{0}}$ $z_{0} = \sqrt{μ_{0} / ε_{0}}$ is the wave impedance of free space with the permeability μ₀ and the permittivity ε₀, c is the velocity of light, and $\vec{r}$ $\vec{r}$ is the radius vector of the observation point [2].

Equations 10.1 and 10.2 show that the larger the time derivative of the antenna current, that is, the higher the change of current in the antenna, the larger the field strengths in the far zone. It is also obvious that the higher the current amplitude in the antenna, the higher the field strength in the far zone.

We also see from Equations 10.1 and 10.2 how the current rise time to its maximum value determines the radiated field pulse as shown in Figure 10.2. The electrical characteristics of resistance and inductance for the LCR will determine the current rate and the antenna-radiated pulse duration. Higher radiation efficiency requires increasing the current in the antenna. An effective LCR requires a special pulse generator to drive a specified large current with the appropriate rate of change through the radiator and tune the LCR electrical characteristics of resistance and inductance.

Determining the correct shape and dimensions of the radiator (the parameter ℓ in Equations 10.1 and 10.2) raises the next problem. A bigger dimension ℓ will produce a stronger radiated field strength. On the other hand, a very large radiator length with respect to the signal duration times the speed of light (cΔt) makes Equations 10.1 and 10.2 inapplicable (they are correct when ℓ ≪ cΔt) and can cause late-time ringing in the radiated signal and make the radiated spectrum narrower.

Because a large distance ℓ separates the ends of the radiator, the pulse generator must supply a driving voltage to the ends. The only known way to do this is to use wires to create a return loop, which then radiates and makes antenna characteristics worse. Thus the last specific objective of the LCR design requires some means to suppress the radiation coming from the return loop and elements of the radiator supplying driving signal from the pulse generator to the radiator.

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FIGURE 10.2
The LCR radiated field only occurs during the antenna current rise and fall intervals Δt. For a direct current pulse the antenna only radiates during periods of current change.

Given these issues, we can examine the LCR design problem from two points of view. First, we need to design an appropriate pulse generator. Second, we have to analyze how the LCR radiates electromagnetic waves and determine which elements of antenna can increase radiation efficiency and which of them obstruct the performance and require elimination if possible.

10.3 LCR Drive Signal Generator Design

The LCR antenna should have a low resistance so that R → 0. This means the driver output resistance should approach zero for more effective power transfer from the exciting signal source to the radiator.

The LCR antenna design presents another special problem. Feed lines from a signal generator to the LCR will have relatively high impedances. The LCR antenna will require a design without separate feed lines to carry the driving signal from the generator to the radiator. Therefore, the exciting pulse generator must be built as a part of the LCR.

The exiting pulse generator must have a low output resistance and an external signal timing capability and electrical stability. In addition, LCR pulse generators must be small in size and have low power consumption. Pulse generators with semiconductor switching elements can completely meet these requirements.

10.3.1 Switches with Bipolar Transistors

The generator with bipolar switches shown in Figure 10.3 is from the U.S. Patent 5 365 240, Nov. 15, 1994 by Harmuth (“Efficient driving circuit for large—current radiator”) [9]. Both Harmuth and Mohamed have experimentally tested such a pulse generator as an LCR driving circuit [5,8].

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FIGURE 10.3
A driving circuit for the LCR represented by the “radiating antenna.” This design uses bipolar transistors as switches. (Adapted from Harmuth, H.F., Efficient Driving Circuit for Large—Current Radiator, U.S. Patent 5 365 240, November 15, 1994.)

As shown in Figure 10.3, when a positive pulse feeds the terminal In 1 and a negative pulse feeds the terminal In 2, the transistors VT2 and VT3 will conduct and a current will flow from the terminal +U via R4 and VT3, the radiating antenna, and VT2 and R3 to ground. The problem starts because the radiating antenna not only radiates but also produces a near field or inductive field; so the radiator acts like an inductor and stores magnetic energy. When the current stops in the transistors, the magnetic energy (stored near the radiator when current flowed through it) returns by means of special diodes D3 and D6 back to the power source. Similar processes occur when the transistors VT1 and VT4 conduct and the antenna produces the opposite polarity impulse. Thus, the stored energy (the energy that does not radiate) does not dissipate but returns back to the power supply and gives the antenna a high efficiency.

The low power consumption and small size of the radiator provide the necessary conditions to use it to develop integrated complementary metal oxide semiconductor (CMOS) UWB localizers. The localizer developers Fleming and Kushner designed a special low-voltage CMOS driver that can drive the LCR and produce sequences of pairs of radiated impulses, the so-called doublets [10,11]. CMOS can drive these small antennas because they do not resonate and work in the current mode. Figure 10.3 shows the radiating antenna principle as discussed above.

10.3.2 Switches with Avalanche Transistors

In spite of the low LCR resistance, the inductance of the radiator makes it very difficult to excite a large current in the radiator quickly, for example, for fraction of a nanosecond. As long as the time constant of the radiator equals the ratio of inductance to the active resistance, which usually is considerably bigger than fractions of a nanosecond, this requires raising the driving voltage at the output of pulse generator. There are a number of possible ways to raise the driving voltage. In the following text, pulse generators with avalanche mechanisms for forming short pulses are discussed.

The output resistance of avalanche transistor pulse generators during pulse shaping decreases to a value of the order of fractions of ohm [12]. The switching time from the blocking state to the maximum open state is within fractions of a nanosecond, and the generated voltage amplitudes can reach hundreds of volts. The change of resistance also helps to reduce the time constant of the current in the antenna and provides the short rise time of the driving pulse.

Pulse generators with avalanche transistors have very low power consumption. This characteristic makes them popular as switches among UWB radar systems developers.

Along with researchers Lukin and Kholod, the authors experimented with LCRs designed with avalanche transistors as switching elements [13,14]. Figure 10.4 shows the basic schematic diagram of an experimental large-current pulse generator [13]. The avalanche transistor VT1 is the key component. An external pulse from the transformer T1 triggers the transistor VT1, which also decouples the avalanche transistor pulse generator from the trigger pulse generator. The capacitor C1 and the resistor R2 provide a reliable shut-off of the transistor and a reliable turn-on when the trigger pulse arrives. The capacitors C2 and C3 serve as energy storage. The resistors R1 and R3 limit the current flowing through the transistor when it turns on. These resistors can also regulate the charge current.

The avalanche transistor switch also gives us an opportunity to create multistage circuits that greatly increase the exciting signal power characteristics.

The circuit shown in Figure 10.5 has seven avalanche transistors connected according to the relaxation circuit and acting as switches [14]. Applying the feed voltage U charges the capacitors that are charged through resistors. Then, on simultaneously closing all seven switches, the seven capacitors charged before to voltage U become connected in series.

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FIGURE 10.4
Lukin, Pochanin, Masalov, and Kholod developed a driving circuit for the LCR represented by the “radiating antenna.” The avalanche transistor VT1 acts as the switch. (Lukin, K.A. et al., “Large current radiator with avalanche transistor switch,” IEEE Transactions on Electromagnetic Compatibility, 1997, 39, 2, 156-160, © 1997 IEEE.)

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FIGURE 10.5
Block diagram of a traveling wave pulse generator using avalanche transistor switches to simultaneously connect charged capacitors to supply voltage U. (Pochanin, G.P. and Kholod, P.V., “LCR with a traveling wave pulse generator,” The Third International Conference “Ultra Wideband and Ultra Short Impulse Signals,” September 18-22, 2006, Ukraine, © 2006 IEEE.)

This connection will produce a voltage pulse with amplitude close to 7 U at the signal generator output terminals connected to the radiating plate. This voltage pulse drives the radiating antenna.

Figure 10.6 shows another version of the traveling wave pulse generator. The voltage applied at capacitors of all seven avalanche transistors must not exceed the avalanche breakdown voltage (∼150 V) to prevent the avalanche cascades from generating in the self-oscillation mode. Holding the transistors below the breakdown condition permits easy turn on when a small base current appears when the voltage increases in the collector. In this design, the central (fourth) switch VT4 receives a collector voltage first to turn on the generator and pulse transformer. The avalanche breakdown creates two waves of current with opposite polarity formed in the central cascade. They go out from this cascade to the neighboring third and fifth cascades and initiate the avalanche breakdown there. Then the second and sixth cascades followed by the first and seventh cascades start simultaneously. Every subsequent cascade releases the energy stored in capacitors by the avalanche switches and adds to the traveling wave energy. Thus, while the drive pulse propagates in the generator toward the radiating antenna, its amplitude increases; this produces the synchronism of the drive pulse arrival at the radiating antenna terminals. We call this a traveling wave pulse generator because the wave process takes place during the formation of the LCR drive pulse.

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FIGURE 10.6
A traveling wave pulse generator LCR schematic. This uses seven stages of avalanche transistors. The input pulse travels across T1 to turn on the voltage on avalanche transistor VT4. The discharge of VT4 sets off the connected switches VT3 and VT5, which then sets off the succeeding stages to form the output voltage pulse to the radiating antenna. (Pochanin, G.P. and Kholod, P.V., “LCR with a traveling wave pulse generator,” The Third International Conference “Ultra Wideband and Ultra Short Impulse Signals” September 18-22, 2006, Sevastopol, Ukraine, © 2006 IEEE.)

The authors and their colleague Kholod, used a feeder line consisting of two segments of coaxial transmission line as a return loop to excite the radiating plate, which had its ends connected to the generator away from each other [13,17]. The segments of the coaxial transmission line were replaced by the traveling wave generator placed inside a metal shield [14]. The pulse generator shown in Figure 10.6 has an advantage because it presents the chance to insert and extend it into a sufficiently long and small diameter shielded box. This produces an LCR with a space distributed power pulse generator, which was built as a traveling wave generator that acts as a return loop and matching sections. Now this places the generator output terminals directly at the ends of the radiating antenna, and this eliminates the return loop as shown in Figure 10.5. This helped achieve the most preferable dipole radiation mode because it made the radiating antenna a straight conductor instead of a loop.

10.3.3 Building Switches with S-Diodes

Experiments show that avalanche transistors can provide higher radiated powers. Problems arise because an asymmetry of the amplitude and time responses of pulses at the emitters and collectors of the switching transistors has undesirable effects and can lead to late-time ringing in the radiated signal.

This asymmetry is eliminated by replacing the three-electrode switches with two-electrode devices such as step recovery diodes [15] and S-diodes [16] for the switching circuits for LCR generators. The term S-diode means semiconductor avalanche diode, also called TRAPATT (transient plasma avalanche transit time) diodes in the United States, avalanche diodes by the Ioffe group (St. Petersburg, Russia), or S-diodes by other investigators at the Tomsk State University (Tomsk, Russia). The diode structures differ from each other, but all have the same principle of operation based on avalanche breakdown as presented by A. Kardo-Syssoev in Chapter 9 of [6].

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FIGURE 10.7
An LCR antenna using an S-diode switch to generate electromagnetic pulses. The components R1, R2, C1, C2, and C3 control the pulse repetition rate. Light-activated switching of D1 can control the pulse formation better than multiple transistors. (Pochanin, G.P. et al., “Large current radiator with S-diode switch,” IEEE Transactions on Electromagnetic Compatibility, 2001, 43, 1, 94-100, © 2001 IEEE.)

The LCR pulse generator shown schematically in Figure 10.7 used S-diodes (diode type AA742B) [17]. A storage battery provided the power supply voltage. A DC/DC high-voltage converter charged storage capacitors C1 and C2 up to the S-diode avalanche breakdown threshold. Resistors R1 and R2 with capacitors C1 and C2 formed the repetition rate controlling circuit. Avalanche breakdown in the S-diode D1 occurred when the applied voltage exceeded the breakdown threshold. The discharge current flowed through the radiating antenna and produced a short radiated electromagnetic pulse.

This circuit in Figure 10.7 produced a pulse voltage of 560 V. The diode design permitted generator synchronization by irradiating a semiconductor crystal with infra-red pulses from a semiconductor laser. Light-activated switching and the small-size DC-to-DC converter supplying the power provided the excitation symmetry and eliminated all cables and wires near the LCR. The radiated signal displayed excellent purity and good power characteristics.

10.3.4 Switches with Silicon Field-Effect Transistors

Because field-effect transistors (FETs) do not store charges, they satisfy a necessary requirement for fast current switching and a way to develop power current pulse generators for LCRs [18].

Figure 10.8 shows the LCR equivalent circuit with the following components: the radiating element inductance L_r; its loss resistance R_r; the radiation resistance R_i; capacitance between the radiating element and the LCR shield C_r; and the pulse generator G with output resistance R_g.

To increase the current I_rad, we must reduce the loss resistance R_r. However, the designer must take into account the following conditions:

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FIGURE 10.8
This LCR equivalent circuit provides a way to determine the physical radiator dimensions and values of the components for a given range of pulse durations.

Aperiodic current. The current in LCR should be aperiodic, which requires

$R_{r} + R_{i} \geq 2 \sqrt{\frac{L_{r}}{C_{r}}} (10.3)$ $R_{r} + R_{i} \geq 2 \sqrt{\frac{L_{r}}{C_{r}}} (10.3)$
Time constant. Because the capacitance C_r should smooth the drive signal, select a value to give a time constant

$(R_{r} + R_{i}) \cdot C_{r} ≪ Δ t (10.4)$ $(R_{r} + R_{i}) \cdot C_{r} ≪ Δ t (10.4)$
Current rise time. The LCR circuit exciting current rise time to the peak value should not be less than the characteristic time of the RL circuit

$Δ t \geq \frac{L_{r}}{R_{r} + R_{i}} (10.5)$ $Δ t \geq \frac{L_{r}}{R_{r} + R_{i}} (10.5)$

The conditions shown in Equations 10.3 and 10.5 mean that the radiator inductance L_r limits the possibility of reducing R_r with a fixed Δt. The lesser the radiator inductance, the lower the R_r possible in the LCR circuit, which will then produce a larger current I_rad.

The radiator inductance L_r largely depends on its length. For example, the simplest radiator that has the form of a wide rectangular plate with length ℓ and width w has an inductance of

L_{r} = \frac{μ_{0}}{2 π} ℓ (\ln \frac{ℓ}{ω} + 0.0 8) (10.6)

$L_{r} = \frac{μ_{0}}{2 π} ℓ (\ln \frac{ℓ}{ω} + 0.0 8) (10.6)$

Equation 10.6 shows how reducing the radiator length reduces the inductance and permits decrease in R_r in Equation 10.5 to increase the antenna current I_rad. Under these conditions the radiated field strengths $\vec{E}$ $\vec{E}$ in Equation 10.1 and $\vec{H}$ $\vec{H}$ in Equation 10.2 change insignificantly. For example, by reducing the radiating element length ℓ by a factor of γ we can reduce its inductance L_r by approximately a factor of γ. Thus we can proportionally reduce the loss resistance R_r and increase the current amplitude in the antenna I_rad by γ times. For the case of the current linear rise in the antenna during the fixed time Δt, the strengths of fields $\vec{E}$ $\vec{E}$ and $\vec{H}$ $\vec{H}$ reduce by a factor of γ due to the reduction of ℓ and simultaneously increase γ times due to the increase of I_rad. This implies that the power density flow in the far zone will not change. Warning: this reasoning is correct only for LCRs with length much less than Δt.c.

The most effective transfer of the drive signal energy from the pulse generator G to the LCR occurs at the impedance match condition where

Z_{a} = Z_{g}^{*}, (10.7)

$Z_{a} = Z_{g}^{*}, (10.7)$

where

The antenna complex impedance Z_a = R_r + R_i + jX_a includes the active parts of the sum of the radiation resistance and the loss resistance, and the reactive part jX_a is determined by the radiator inductance.
The exciter pulse generator complex impedance Z_g = R_g + jX_g includes the drive signal source consisting of the active part R_g and the reactive part X_g.

For matching the pulse generator and antenna, we can write the conditions of Equation 10.7 as

{\begin{matrix} R_{r} + R_{i} = R_{g} \\ X_{a} = - X_{g} \end{matrix} (10.8)

${\begin{matrix} R_{r} + R_{i} = R_{g} \\ X_{a} = - X_{g} \end{matrix} (10.8)$

In practice, the active part of the output resistance of power pulse signal generators, built with power microwave semiconductor elements and having nanosecond pulse durations, usually amounts to a few tens of ohms. To satisfy the first condition of Equation 10.8—while taking into account that the LCR radiation resistance is no more than several ohms and the loss resistance in the radiating element conductor amounts to fractions of an ohm—it is necessary to insert the additional resistor R_d in series with R_r and R_i in the LCR exciting circuit, so that

\begin{matrix} R_{r} + R_{i} + R_{d} = R_{g} \end{matrix} (10.9)

$\begin{matrix} R_{r} + R_{i} + R_{d} = R_{g} \end{matrix} (10.9)$

This means the output resistance of the signal drive R_g source limits the possibility of increasing I_rad.

By taking the above-mentioned conditions into account, a tunable LCR can be developed. To radiate pulses with duration ranging from Δt_max to Δt_min, according to condition 10.5, the maximum allowable inductance of the radiator should be limited so that

L_{r \max} \leq R_{g} \cdot Δ t_{\min} (10.10)

$L_{r \max} \leq R_{g} \cdot Δ t_{\min} (10.10)$

Then, the radiator form and dimensions can be selected by using the conditions that relate the radiating element dimensions to its inductance (e.g., Equation 10.6 gives the inductance for a wide plate). The best radiator will have the largest length ℓ because it has the highest radiation resistance R_i.

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FIGURE 10.9
This four cascade power pulse generator can increase the radiated field strength to achieve radiator symmetrical excitation. This can switch the current on and off in pairs of radiators symmetrically.

The value of the additional resistor R_d can be determined from Equation 10.9 based on the choice of the radiator length and calculation of its radiation resistance from R = (Z₀/6π)((l²/(c·Δt)²) [2,5] for a pulse with maximum duration Δt_max from the duration range.

As a rule, the value of the capacitance C_r shown in Figure 10.8 cannot be calculated beforehand owing to the lack of equations that allow easy calculation of the capacitance of arbitrary shaped conductors (we can calculate capacitances only for a limited number of conductor’ shapes). Therefore, it becomes necessary to follow the requirements of Equation 10.4 and try to make this capacitance minimal.

To increase the radiated field strength and to achieve radiator symmetrical excitation, we can use the pulse generator shown in Figure 10.9. This unit has four cascades that can switch the current on and off in pairs of radiators symmetrically.

In the first pulse power generator of Figure 10.9, an external pulse generator drives the preamplifier with the transistor VT1. The second pulse generator forms impulses of equal amplitude and opposite polarity by exciting a phase inverter with the transistor VT2 at the 2 outputs. Then, each of the phase inverter outputs drives a pair of power amplifiers. Power amplifiers 1-4 generate current pulses I_rad1 − I_rad4 of the trapezoidal form with the rise and the decay time equal to Δt, shown in Figure 10.10 in the radiating antennas 1−4. These currents point in space in such a way that I_rad1 and I_rad2 are in-phase, co-directional, and directed opposite to reversed phase currents I_rad3 and I_rad4 as shown in Figures 10.10 and 10.11. T hese conditions provide for the summing of field strengths from four radiating antennas $\vec{E_{1}} + \vec{E_{2}} + \vec{E_{3}} + \vec{E_{4}}$ $\vec{E_{1}} + \vec{E_{2}} + \vec{E_{3}} + \vec{E_{4}}$ in far zone.

The driving generator can operate both in switch mode (assuming the rise and fall times of pulses were minimal and depended on transistor characteristics), and in linear amplification mode (assuming the rise and fall times of pulses were more than in switch mode and they were specified by the external generator).

The generator modes allow programming a whole series of LCR operating conditions with antennas with several radiators that promote a more thorough understanding of LCR excitation and electromagnetic field radiation.

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FIGURE 10.10
Timing diagrams of the exciting currents and radiated fields for the four cascade power pulse generator shown in Figure 10.9.

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FIGURE 10.11
The radiating field operating principle of the four-element radiator of the tunable LCR driven by the four cascade power pulse generator of Figure 10.9 with the timing shown in Figure 10.10.

10.3.5 Switches With GaAs FET

The supply voltage and power consumption of power pulse generators can be reduced by using GaAs FET as switching elements (shown in Figure 10.12a and b). The on-state resistance of this transistor approaches 0.5 Ω, which causes a large current to flow in the radiating antenna of the LCR.

The driving circuit of the antenna shown in Figure 10.12a represents two switches with the high-power field-effect GaAs transistors (VT3 and VT4) connected in series with the radiated antenna. (This circuit is similar to a half of the driver shown in Figure 10.3.) By operating together they provide balanced antenna excitation.

Two 51-Ω resistors R14 and R15 are connected in parallel with the transistors VT3 and VTS (between the source and drain) to fix the potential on the drains of VT3 and VT4. These resistors work together with the diode D1 to promote the decrease of the voltage overshoot at the instant of switching off VT3 and VT4. The resistor and diode attenuate oscillations occurring in the antenna after switching off VT3 and VT4. Notice how the connection of R14 and R15 increases the power consumption by 50 mA for each driver, but we have to accept this penalty.

As the resistance of two fully open transistors VT3 and VT4 is approximately equal to 1.2 Ω, R14 and R15 do not shunt the antenna during excitation. Almost the whole current exciting the antenna flows through the circuit from “+” of the power supply to VT3, to the radiating antenna, to VT4, to the ground.

10.3.6 Microcircuits as Switches

High-speed digital integrated circuits include microcircuits that can work as switches in an LCR. Thus, for example, Prof. H.F. Harmuth has proposed using the Texas Instruments^TM SN74BCT25244-D that has 25-Ω buffers/drivers with 3-state outputs and 8 outputs. Each of these outputs can switch a current up to 160 mA for a time in the order of 1 ns at a 5 V supply voltage. Figure 10.13a shows four of these microcircuits set to drive an LCR antenna. If a positive pulse comes to Input A and a negative pulse comes to Input B then the terminal of R1 connected to the microchip has a voltage +U/2 and the terminal of R2 has a voltage −U/2. This condition allows current flow through the radiating antenna. Changing the pulse polarity at Input A and Input B reverses the current in the radiating antenna. This permits the LCR to radiate positive and negative field strength pulses. Increasing the number of microchips increases the current amplitude in the radiator. The four microchips (two on Card A and two on Card B) can drive 16 radiating antennas in experiments as shown in the device in Figure 10.13b.

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FIGURE 10.12
A pulse generator using GaAs field effect transistors (FETs) can reduce the power supply voltage and power consumption. (a) The GaAs driver circuit with FETs VT3 and VT4. (b) The physical circuit.

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FIGURE 10.13
(a) Schematic diagram of pulse generator using Texas Instruments SN74BCT25244-D microcircuits which have 25-Ω buffers/drivers with 3-state outputs and eight outputs. Each of these outputs can switch the current up to 160 mA for the time of the order of 1 ns at supply voltage 5 V. (b) Card A of the driver exciting 16 radiating antennas.

The only problem is that the outputs of this microcircuit cannot connect to the same load in parallel. That is, only one radiator can be connected to each of the microcircuit outputs. Therefore, number of radiators should be increased for increasing the current in LCR. However, this causes problems of achievement of simultaneous switching of all drivers due to the coupling between radiators, which are loads for the microchips SN74BCT25244-D. Section 10.4 of this chapter will consider these emission synchronization problems.

10.3.7 LCR Excitation Conclusions

The earlier subsections of Section 10.3 discussed various LCR excitation circuits based on different types of switches. We can conclude the following:

Diode pulse generators give the simplest and at the same time energy-optimal excitation circuits for LCR.
Somewhat inferior to S-diodes because of the asymmetry of the generated signal circuits with switches on avalanche transistors.
Circuits with FET switches require more power and need an additional protection from breakdown due to surge overvoltage.

The effective excitation of the low resistance and large inductance LCR becomes possible because the pulse generator output resistance changes within a wide range during pulse forming when there is a direct connection between the pulse generator and radiating element. This integrated configuration decreases the time constant of the antenna exciting circuit and promotes matching of impedances between the pulse generator and radiator. This combination of sudden resistance drop and impedance matching provides effective LCR antenna excitation.

10.4 Antenna Designs for Radiating UWB Pulse Electromagnetic Fields

Section 10.3 discussed the different kinds of pulse generators for LCR excitation. However, the pulse generator design is only part of the problem. The development and construction of a matching radiator presents a much more difficult problem: how to find the antenna geometry that can most effectively convert the energy of the electrical impulses coming from a generator into the radiated electromagnetic field?

In the previous section we analyzed the control capabilities of one of the changeable parameters in Equations 10.1 and 10.2, specifically the current amplitude I_rad. In this section we examine the effects of changing the radiating antenna length l.

The LCR concept described in Section 10.2 now requires theoretical and experimental searches for approaches that will permit large current switching in the radiating element along with the dipole radiation mode. This requires new investigations of the nature of electromagnetic wave radiation and the search for better shapes and sizes of the radiating element. AetherWire and Location (USA) has made considerable contributions to LCR development. These efforts resulted in the Sanad U.S. Patent “Ultra-wideband monopole large current radiator” [19], which suggests a conversion of the mode of the LCR radiation from dipole to monopole. The Sanad patent claimed different shapes of radiating elements shown in Figure 10.14 including a conductor with a metal shield located near the radiating element as shown in Figure 10.14c. Theoretical estimates that have been done by the author demonstrated the potential performance of the proposed antennas, as well as a way to reduce the level and amplitude of late-time ringing in radiated signals.

Although the Sanad patent outlines a range of possible sizes of radiators, it gives no clear criteria relating the effectiveness of radiation with the size of the radiator [19]. The relation between dimensions of the radiator and time parameters of the exciting pulses and their influence on the shape of the emitted pulse also require special consideration.

10.4.1 UWB LCR Antenna Dimensions

The next part of this chapter discusses the investigations on the influence of geometrical parameters and corresponding structural parameters on characteristics of radiated electromagnetic field pulses.

From Equations 10.1 and 10.2, we see that the radiated field strength depends directly on the radiating antenna length. However, remember these idealized expressions assumed a small radiating antenna length and little change in the current amplitude within the whole radiator. In addition, these equations fail to account for the fact that the exciting antenna circuit requires a closed circuit in order to permit a large current. Now all the simplified assumptions disappear and we start to learn how things really work.

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FIGURE 10.14
The search for better LCR antenna geometries. (a−d) Examples of patented radiators’ geometries by M.S. Sanad. (Adapted from Sanad, M.S., Ultra-wideband Monopole Large Current Radiator, U.S. Patent 6 650 302 B2, November 18, 2003.)

The authors along with colleague Kholod studied the influence of the actual radiator geometry (shown in Figure 10.15) on the characteristics of radiated electromagnetic field pulses. They performed electrodynamic finite-difference time-domain (FDTD) simulations of UWB pulse radiation for an asymmetrical loop LCR [20,21]. Their analyses used the LCR antenna coordinate system shown in Figure 10.15. The coordinate origin starts at the radiating plate (radiating antenna) center. The plate lies in the plane ϒ = 0, and the exciting current goes in the direction of the Z-axis. The driving pulse has a Gaussian shape with a 1-ns duration. The simulations help to analyze how the LCR characteristics such as the radiating plate width w, the matching section length d, and the radiating element length ℓ influence the radiated field intensity.

10.4.1.1 How Will the Radiating Plate Width Affect the Radiated Field Pulse?

The simulation was started by setting the length ℓ = 40 mm and the matching sections length d = 30 mm. Then it was determined how the current pulses in the generator changed as the width w varied from 4 to 160 mm. Figure 10.16a shows the current pulses in the generator when connecting radiators with the radiating plate width 4, 40, and 160 mm. One can see that when the radiating plate width increases, the current pulse rises, the decay time reduces, and the pulse amplitude goes up.

Images

FIGURE 10.15
Masalov, Pochanin, and Kholod used this LCR coordinate system and dimensions to evaluate the effects of antenna geometry on the effectiveness of pulse radiation. (Adapted from Masalov, S.A. et al., “UWB loop receiving and transmitting antennas,” in A. Y. Grinev (Ed.), Questions of Subsurface Radiolocation, Radiotekhnika, Moscow, 344-372, 2005. (In Russian).)

Meinke and Gundlach described the inductance ℓ of the flat plate with length ℓ, width w, and thickness δ (the dimensions are specified in cm) as $L = 2 ℓ (ln (2 ℓ / (w + δ)) + 0.447 ((w + δ) / 2 ℓ) + \frac{1}{2}) (nH)$ $L = 2 ℓ (ln (2 ℓ / (w + δ)) + 0.447 ((w + δ) / 2 ℓ) + \frac{1}{2}) (nH)$ [22]. Increasing the conductor width resulted in reducing its inductance which decreased the current rise time in the circuit. When the driving pulse rises and decay time is less than the antenna time constant L/R (where R is the generator output resistance), then decreasing ℓ results in increasing the current amplitude in the radiator.

Figure 10.16b shows the dependence of k(w) = I_max(w)/I_max (w = 4), which is a coefficient showing how the maximum amplitudes of the pulse current in the antenna at different values of width ω (I_max(ω)) depends on the pulse current amplitude at ω = 4 mm (I_max (ω = 4)). It also allows us to analyze whether it is possible to make the current pulse amplitude larger by means of widening the radiating plate and by how much. This shows the most considerable increase of the current pulse amplitude at the increase of w from 4 to 60 mm. Later on, the rate of increase begins to slow down. Figure 10.17 trace 3 shows the calculated pulses of the electric field strength at distance D = 1.2 m in the direction of the ϒ-axis when w = 160 mm and k = 1.42. The minimum pulse amplitude corresponds to the radiator widths w = 4. The tenfold increase of w up to 40 mm results in increasing the field intensity by 1.5 for the electric component and by 1.3 for the magnetic component. The further increase of w up to 160 mm will lead to the increase of the field intensity by 1.8 for the electric component and by 1.44 for the magnetic component with respect to the LCR design with w = 4 mm.

Figure 10.18 shows diagrams of how the maximum amplitude of the field created by the radiator with width w compares with the radiator with width w = 4 mm both for the electric field component m = E_max(w)/E_max (w = 4) and for the magnetic field component n = H_max(w)/H_max (w = 4). The greatest effect is observed at the increase of the antenna width up to 60 mm; further increase of w has less influence on m and n.

The increase of the $\vec{E}$ $\vec{E}$ and $\vec{H}$ $\vec{H}$ field intensities with increasing w is typical of all field components except for the field $\vec{H}$ $\vec{H}$ near the radiator. In this case, as w increases the field intensity begins to increase first, and then it decreases after reaching w = 40 mm. The current amplitude distribution on the radiating plate width causes this dependence of the field amplitude H. We can observe the maximum current amplitude of a fast process in flat plates on edges of these conductors. By widening the radiating plate we remove the edges from the point of observation, which sits near the radiating plate center, and thereby decrease the magnetic field pulse amplitude at this point. As the distance D increases, this effect has less influence on the radiated pulse intensity. As a result, at long distances from the radiator the increase of w leads to the increase of the pulse amplitude.

Images

FIGURE 10.16
FDTD analysis of the antenna in Figure 10.15 examined the effects of (a) the current pulses in the radiator for length l = 40 mm, the matching sections length d = 30 mm, and width (1) w = 4 mm, (2) w = 40 mm, (3) w = 160 mm; (b) the variation of k(w) = I_max(w)/I_max(w) = 4 mm) with the antenna width w.

Images

FIGURE 10.17
The effect of antenna radiator widths on calculated electric field pulses. This shows the calculated electric field at a distance of 1.2 m from the radiator for which length £ = 40 mm, the matching sections length d = 30 mm, and width (1) w = 4 mm; (2) w = 40 mm; and (3) w = 160 mm.

Images

FIGURE 10.18
The dependence of the (a) electric and (b) magnetic field ratios m and n on the radiating plate size ℓ = 40 mm, the matching sections length d = 30 mm, and width w for the fields $\vec{E}$ $\vec{E}$ and $\vec{H}$ $\vec{H}$ . Increasing the radiator width up to 60 mm has the greatest effect. Any further increase of w has less influence on m and n.

Note that for the magnetic field ratio n = H_max(w)/H_max (w = 4) in Figure 10.18 shows the plot for D = 1.2 m, which coincides almost accurately with the plot of k(w) shown in Figure 10.16b. Consequently, we can assume that the increase of the radiated field pulse amplitude only results from increased current pulse amplitude. Note the decreased n(w) at close distance D = 0.1 m as the width increases.

10.4.1.2 How the LCR Radiated Field Pulse Depends on the Matching Section Length

To determine the effects of the matching section length on the LCR radiated field pulse, we set ℓ = 40 mm and w = 40 mm. Then we change the matching section length d shown in Figure 10.15 from 10 to 160 mm. Figure 10.19 shows the calculated electric field pulse intensities at distance D = 1.2 m. The minimum pulse amplitude corresponds to the radiator with d = 10 mm shown in trace 1. The fourfold increase of d up to 40 mm doubles the field intensity shown in trace 2. Increasing d up to 80 mm results in increasing the field intensity by 2.75 times shown in trace 3. The further increase of d leads to the onset of oscillations in the radiated signal shown in traces 4 and 5; however, the increase of the radiated pulse amplitude is insignificant.

When d = 100 mm it means that the radiator perimeter approaches the spatial pulse duration χ, which causes the onset of oscillations in the antenna due to resonance effect.

An increase in d accompanies the increase of the radiated pulse rise and decay time. When d = 10 mm, the radiated signal rise time reaches its first extremum at a time point of 5.84 ns and when d = 80 mm, at a time point of 6.1 ns shown in Figure 10.19. The difference is about 0.26 ns. This value multiplied by the velocity of light gives 78 mm and is close to the difference of the matching section lengths. Consequently, the distance between the loop bends in the observation direction influences the radiated signal rise and decay time.

The maximum radiation emerges at the region where the loop bends. The radiated electromagnetic field forms from the interference of the outgoing fields from all four bends and the radiator excitation region. We conclude that by spacing these strongly radiating regions we can change the time delay between radiation moments of each of these regions and, respectively, between the moments of radiation emerging from each of the regions into the observation point. Thus, through the delay arising from the increase of d, the maximum amplitude of the radiated field pulse shifts along the time axis from the pulse point, thereby increases the radiated signal rise time.

Figure 10.20 shows how the matching section length d compares with the maximum amplitude of the field created by the radiator with d = 10 mm both for the electric and magnetic field components: m(d) = E_max(d)/E_max(d = 10) and n(d) = H_max(d)/H_max(d = 10). These diagrams show that the increase of d up to 40 mm leads to the increase of the field intensity near the radiator, but at greater matching section lengths d produces no significant growth. Increasing d up to 0.1 m results in a linear growth of the field amplitude in the far zone. After d = 0.1 m, the radiator shows the onset of oscillations in the radiated signal.

Images

FIGURE 10.19
Pulses of the electric field E at a distance of 1.2 m from the radiator of Figure 10.15 with ℓ = 40 mm and w = 40 mm for the matching sections lengths (1) d = 10 mm; (2) d = 40 mm; (3) d = 80 mm; (4) d = 100 mm; (5) d = 120 mm. Note that increasing d greater than 100 mm results in oscillations after the transmitted pulse.

Images

FIGURE 10.20
The dependence of m(d) and n(d) on the length of matching sections d for the (a) electric $\vec{E}$ $\vec{E}$ and (b) magnetic $\vec{H}$ $\vec{H}$ fields for the LCR with ℓ = 40 mm and w = 40 mm. This occurs because the radiated electromagnetic field forms from the interference of the outgoing fields from all four bends and the radiator excitation region.

Thus, the increase of d is accompanied by the increase of rise and decay time of the radiated field pulse. With increasing d the field pulse amplitude increases fast at first, and then this growth slows down. Starting from the value d, at which the radiator perimeter becomes equal to spatial pulse length χ, the radiator goes into oscillatory mode.

10.4.1.3 How the Radiated Field Pulse Parameters Depend on the Radiating Plate Length

To show the dependence of the field on the radiator plate length, d is set at 30 mm, w at 40 mm, and the radiating plate length ℓ is increased from 10 to 200 mm. Figure 10.21 shows the electric field pulse intensities at distance D = 1.2 m.

Images

FIGURE 10.21
The electric field pulses at a distance of 1.2 m from the radiator with d = 30 mm, w =40 mm for lengths (1) ℓ = 10 mm; (2) ℓ = 40 mm; (3) ℓ = 80 mm; (4) ℓ = 100 mm; (5) ℓ = 120 mm; (6) ℓ = 160 mm; (7) ℓ = 200 mm. Increasing the growth of ℓ produces an increase of the pulse rise and decay time similarly as it was at the increase of d.

Images

FIGURE 10.22
The ratio of electric $\vec{E}$ $\vec{E}$ (a) and magnetic $\vec{H}$ $\vec{H}$ (b) field maximum amplitudes from a radiating plate length ℓ for distances to the observation point D = 0.1, 0.3, and 1.2 m.

Increasing the size of the radiator length ℓ produced a longer pulse rise and decay time, the same effect that resulted from increasing the depth d. As shown in Section 10.4.1.2, an increase in d increases the rise and decay time because of the larger distance between strongly radiating regions.

Increasing ℓ beyond 100 mm leads to the onset of oscillations in the radiated signal as shown in Figure 10.21 traces 4−7 (100−200 mm). Here, the radiated pulse amplitude continues to increase. When ℓ = 120 mm, the radiator perimeter approaches the spatial pulse duration χ, this creates the conditions for the onset of oscillations.

Figure 10.22 shows the relations of the maximum electric m(ℓ) and magnetic n(ℓ) field amplitudes for a radiator with an increased dimension ℓ with respect to a radiator of dimension ℓ = 10 mm. These diagrams show that the increase of ℓ near the radiator leads to a practically linear increase of the field intensity. But it follows from Figure 10.21 that if it is necessary to radiate a “clear” signal the length of the radiating plate should be ℓ = 120 mm. For the case ℓ > 120 mm the radiator goes into oscillatory mode and the electric field amplitude increases only fourfold.

10.4.1.4 LCR Design Conclusions

The antenna designer can conclude that for the LCR of Figure 10.15

The rise and decay time of the radiated field pulse increases with ℓ.
The field pulse amplitude increases practically linearly with ℓ.
When the value of ℓ reaches a point where the radiator perimeter becomes equal to the spatial duration of the pulse χ, the LCR antenna goes into an oscillatory mode.
The increase of the radiated pulse intensity with increase in LCR dimension w results from the increased current amplitude, which results from the decrease of the antenna inductance.
The radiated field pulse forms from the interference of four pulse electromagnetic waves radiating from the loop bends and waves emerging in the excitation region.
Increasing the matching section length d and increasing the radiating plate length ℓ will increase the rise and decay times and the radiated pulse amplitude. Note that the increase of ℓ causes a threefold increase of the amplitude.

As per the design rule, we can determine the maximum allowed values of LCR dimensions for a radiator excited by a Gaussian pulse with a rise (fall) time Δt as

Maximum allowable matching sections length d < (c · Δt/2)−ℓ
Maximum allowable radiating plate length ℓ < (c · Δt/2)−d

Exceeding these conditions will produce oscillations in the radiator and, consequently, late-time ringing in the radiated signal.

10.4.2 LCR Antenna Near- and Far-Field Characteristics

The theory presented by Harmuth [2,5] shows the dependence of radiated electric and magnetic field strengths on distance as follows:

\vec{E} = \frac{Z_{0} ℓ}{4 π c} [\frac{1}{r} \frac{d I_{r a d}}{d t} \frac{\vec{r} \times (\vec{r} \times \vec{ℓ})}{ℓ \cdot r} + (\frac{c}{r^{2}} I_{r a d} + \frac{c^{2}}{r^{3}} \int I_{r a d} d t) (\frac{3 (\vec{ℓ} \cdot \vec{r}) \cdot \vec{r}}{ℓ \cdot r^{2}} - \frac{\vec{ℓ}}{ℓ})] (10.11)

$\vec{E} = \frac{Z_{0} ℓ}{4 π c} [\frac{1}{r} \frac{d I_{r a d}}{d t} \frac{\vec{r} \times (\vec{r} \times \vec{ℓ})}{ℓ \cdot r} + (\frac{c}{r^{2}} I_{r a d} + \frac{c^{2}}{r^{3}} \int I_{r a d} d t) (\frac{3 (\vec{ℓ} \cdot \vec{r}) \cdot \vec{r}}{ℓ \cdot r^{2}} - \frac{\vec{ℓ}}{ℓ})] (10.11)$

\vec{H} = \frac{ℓ}{4 π c} (\frac{1}{r} \frac{d I_{r a d}}{d t} + \frac{c}{r^{2}} I_{r a d}) \frac{(\vec{ℓ} \times \vec{r})}{ℓ \cdot r} . (10.12)

$\vec{H} = \frac{ℓ}{4 π c} (\frac{1}{r} \frac{d I_{r a d}}{d t} + \frac{c}{r^{2}} I_{r a d}) \frac{(\vec{ℓ} \times \vec{r})}{ℓ \cdot r} . (10.12)$

It follows from Equations 10.11 and 10.12 that fields formed by the LCR have components of different physical nature. The $\vec{E}$ $\vec{E}$ and $\vec{H}$ $\vec{H}$ components are inversely proportional to distance r and are responsible for the radiated field. The induction field has related components proportional to the current in the antenna and which decrease as 1/r² when distance r increases. There is also a component that characterizes the energy of the driving signal that is proportional to the time integral of the current and decreases as 1/r³.

Although computer simulations of electromagnetic processes greatly simplify the investigation of the performance prediction of LCRs, we need to use direct physical experiments to demonstrate the effects. A well-designed experiment helps discover the physical mechanism of electromagnetic radiation and then find a way to increase radiation efficiency. The LCR has suitable qualities for such investigations.

It turns out that we can observe the behavior of field components of the LCR when the antenna driving has a trapezoidal voltage pulse with a flat top that significantly exceeds the rise and decay time. The experiments described here will use this signal as shown in Figure 10.2.

The experiment used a pulse generator as shown in Figure 10.12 to excite the LCR. The generator has an output resistance ∼1.2 Ω. The LCR connects directly to the generator output as shown in Figure 10.23. The LCR radiating plate had dimensions of length ℓ = 40 mm and width w = 40 mm. In the course of experiments we measured the field pulses parameters at distances r ranging from 0.1 to 1.5 m in 0.1 m increments under antenna excitation by 15 ns pulses. Voltage waveforms at the output of magnetic receiving antenna [23] correspond to measured magnetic field strengths. Conversion factor from voltage to field strength equals to 0.3 A/m/V.

Images

FIGURE 10.23
The LCR with the 15 ns pulse generator used for experimental measurements. LCR radiating plate dimensions: length ℓ = 40 mm; width w = 40 mm; perimeter ≈150 mm.

10.4.2.1 How the Field Pulse Parameters Depend on Distance

Figure 10.24 shows the magnetic field strengths measured from the antenna and pulse generator of Figure 10.23. The diagrams represent both the near fields and the far fields and show the process of shaping the radiated field pulse.

When r = 0.1 m the field pulse almost repeats the pulse form of the antenna-driving current. The pulse form has two distinctive sections with a short pulse rise and a long pulse rise. The section with the short pulse rise time occurs from 3.5 ns to 4 ns and has a 1.7 mV amplitude. The section with the long pulse rise time lasts for 17 ns and has a 9 mV amplitude.

The whole length of the experimental radiator (perimeter) in Figure 10.23 is ≈ 150 mm. The field pulse driving the radiator runs over this distance nearly for 0.5 ns. In the experiment the rise time of the driving pulse was 0.7 ns. This time is comparable with the time of its propagation along the whole antenna. Therefore, during almost the whole rise time, the antenna can be considered as a system with distributed parameters. Only after the short pulse process does the antenna start operation when the current flows through the whole antenna, and its inductance affects the current rise time. Starting from this moment when the inductance affects the rise time, we can use the lumped parameters of the antenna to determine time characteristics of the driving current.

Following the rapid growth observed a slight decrease (about 10% of the amplitude of the fast front) is observed. The following long pulse rise indicates that the whole inductance of the radiator is engaged in the pulse forming. In most electrical modeling, we use the inductance ℓ as a constant. Now, we find that the LCR case inductance becomes a function of time L(t). The antenna current rise time in the antenna now varies as L/R, where ℓ is the radiator inductance and R is the output on-resistance of the pulse generator. In the course of the current rise time in the radiator (when ℓ = 40 nH and R = 1.2 Ω, the current rise time in the loop is −33 ns) and during the whole time of the driving signal, that is, about 15 ns, the inductive field stores energy.

Examining Figure 10.24 shows how when the range r increases up to 0.2 m, the relative amplitude of the slow pulse becomes lower. When r = 0.3 m amplitudes of sections with the short and long rise time of the pulse become even. After that a short pulse separates from the remaining slow part of the field pulse.

Images

FIGURE 10.24
Measured plots of magnetic field strengths of the LCR in Figure 10.23 excited with a 15 ns pulse. These show how the field pulse changes when it moves away from the radiator.

The faster amplitude decrease in the slow part of the field pulse is a distinctive effect that accompanies the further increase of the distance to the observation point within 0.3 m ≤ r ≤ 0.9 m. As a result, when r = 0.9 m there are only short pulses remaining in the radiated field that are generated by the fast current in the radiator.

The field strength versus distance plots in Figure 10.24 show that the radiated field pulse is formed during the rapid process. During the slow process the energy is stored as a magnetic field in the near field of the radiator. After the generator switches off, this part of energy of the driving signal stimulates the appearance of electromotive force (EMF) of induction in the antenna terminals.

In Figure 10.25a and b the amplitude values of the field pulses at corresponding distances r are marked with points. Figure 10.25a also shows the plot of U(r) ~ 1/r. Starting from r = 0.6 m, amplitude values of the short field pulse coincide much with corresponding values in the graph. This dependence is typical both of the radiated field and the far zone.

Figure 10.25b shows the measured magnetic field strength as functions of range U(r) ~ 1/r² and U(r) ~ 1/r³. The amplitude values of the slow part of the radiated pulse are between these curves nearer to the last one. The slow part of the field pulse is the near-zone field of the measured antenna.

Images

FIGURE 10.25
Measured peak amplitudes of magnetic fields for the experimental antenna of Figure 10.23. These show the dependence of the amplitude on distance r for (a) the fast part of the field pulse and (b) the slow part of the field pulse.

It should be noted that at long distances (r ≥ 0.9 m) the radiated field pulse is close in shape to the unidirectional one. It has a short positive part with amplitude exceeding considerably the amplitude of a longer negative part.

10.4.2.2 How the Field Pulse Parameters Depend on the Radiating Plate Length

In the next experiment, we compared the pulses of the magnetic field H, generated by radiators with a small radiating element (ℓ = 10 mm) and with a large radiating element (ℓ = 40 mm). The spatial dependence of the amplitude ratio of the short field pulses generated by the small (U1) and the large (U2) radiators shown in Figure 10.26 “fast part” has special interest. At short distances (e.g., 10 cm) this ratio is small (about 1.5), but when the distance increases the ratio increases as well and tends to become 4. This plot shows the ratio of lengths of the large and the small radiating elements. Equations 10.11 and 10.12 define the dependence of the electrical and magnetic pulses at long measurement distance r.

The curve “slow part” shows the spatial dependence of the ratio of slow field strengths, generated by the small (U1) and the large (U2) radiators. At the distance of 10 cm this has a ratio of about 1.7. When the distance increases, the ratio first increases and then decreases. This decline results because the inductance of the small radiator is 3.5 times smaller than that of the large radiator, which produces a shorter small radiator current rise time. During the driving pulse duration, the current in the small radiator amounts to its maximal value and the field strength of the slow process has the maximal amplitude. Owing to the relatively large inductance in the large radiator the current rise time is greater than the driving signal duration, which cuts off the driving signal before the current amplitude reaches its maximum value. As a result, we have the ratio of field strengths 1.7 instead of the expected value 4. When the distance increases, this value also increases a bit and then approaches 1.

These experimental results demonstrate the different nature of LCR in the near and far fields. We have shown that the near field is the inductive field of the LCR. For example, this interpretation implies that we can move the far-zone boundary by changing the quantity of energy stored in the inductance.

Images

FIGURE 10.26
The ratio U2/U1 of measured magnetic field pulse signal amplitudes radiated by large U2 (ℓ = 40 mm) and small U1 (ℓ = 10 mm) radiators. Notice how the slow part decreases after a distance of about 15 cm.

While moving away from the radiator, the ratio of amplitudes of the radiated field pulses generated while driving the large and the small radiator by the high-speed current drops, increases, and depends on the ratio of radiator lengths. At the same time, with increasing r the ratio of field strengths generated by the slow part of the driving current quickly approaches 1. This indicates that for the LCR the near-zone boundary is determined largely by driving signal time characteristics instead of the radiator sizes.

10.4.2.3 How the Field Pulse Parameters Depend on the Value of Active Resistance in the Radiating Element Circuit

The author’s work included experimental results showing how to reduce the near-field component by controlling the radiator current without greatly influencing the far-field component amplitude [20]. The following experiments show this effect. As a first step, the radiating antenna was connected to the driver directly, and the field pulse parameters were measured at separations from 10 to 120 cm in 10-cm steps after exciting the antenna with pulses of 15, 35, and 55 ns duration. The results obtained apply when antenna circuit resistance in the antenna circuit equaled 1.2 Ω. Two resistors R1 and R2 of 1 Ω each were then inserted in series with the radiating antenna. (Figure 10.27 shows a fragment of the output part of the driver circuit.) As a result, the resistance in the antenna circuit became equal to 3.2 Ω. Similar field pulse measurements were again carried out. Two 4.7 Ω resistors were then connected in series with the radiating element, which resulted in the resistance in the antenna circuit to be equal to 10.6 Ω, and the field pulse parameters were measured again.

Figure 10.28 shows how the radiator circuit resistance can strongly influence the near-field components. At the top trace (a) for R = 1.2 Ω, the near-field components can be easily seen even at distances of 90 cm, whereas at the center trace (b) for R = 3.2 Ω, the near-field components have diminished considerably less, and at the bottom trace (c) for R = 10.6 Ω, the near-field components appear to be practically negligible.

The purest observed pulse is when R = 10.6 Ω. Both the leading and trailing edges of the driving pulse form relatively pure pulses. The antennas with R = 3.2 Ω and especially with R = 1.2 Ω have oscillations in the time interval between pulses of the leading and trailing edges and after them. Moreover, the antenna with R = 1.2 Ω has a quite higher relative level of oscillations.

Images

FIGURE 10.27
Fragment of the output part of the driver circuit in Pochanin’s experiments with reducing the LCR near-field component by adding resistors to the radiator circuit.

Figure 10.29 shows how the amplitude of a short pulse forming the radiated signal depends on the distance for antennas with resistances R = 1.2, 3.2, and 10.6 Ω. The curves are very close. Figure 10.30 shows the ratio of the signal amplitudes U_1.2Ω/U_10.6 for antennas with resistance R = 1.2 Ω compared with antennas with R = 10.6 Ω, and the ratio U_3.2Ω/U_10.6 of the signal amplitude for antennas with R = 3.2 Ω compared with antennas with R = 10.6 Ω. It can be seen that the antenna with R = 10.6 Ω radiates a signal 1.2 times smaller at the average in comparison with the antenna with R = 3.2 Ω and 1.4 times smaller at the average in comparison with the antenna with R = 1.2 Ω. The advantage in amplitude of antennas with low resistance is not high, but they radiate less pure pulses in comparison with the antenna with R = 1.2 Ω.

From these results, the following interesting observation can be derived. When amplitudes of pulses radiated by the single radiator at the series-connected resistances were compared, it was noted that by increasing the resistance caused the radiated field pulse amplitude to decrease not proportionally to the resistance value but in another manner. When the resistance increased nearly tenfold the radiated field pulse amplitude decreased only by a factor of 1.4. Increased resistance produced a rapid decay of the near-field component amplitude. This effect results from the decreased antenna current amplitude. But the nonproportional decrease of the field pulse amplitude at the increased resistance needs to be explained.

By convention, the near-zone boundary is the distance at which the far-field strength is equal in amplitude to the near-field strength [2]. The near-field strength increasingly depends on the radiator current, so the far-field boundary can be shifted within certain limits. So, in spite of the dependence on the radiator current, antenna experts can usually control the far-field boundary distance.

10.4.3 How Return Loop Shielding Affects LCR Radiation

To prevent compensating field radiation by the return loop, it is necessary to shield this element of the LCR. Harmuth, Mohamed, and Hussain [1-5,7,8] used planar ferrite or metal-ferrite shields to separate the half-space with radiator from the half-space with the return loop in Figure 10.1 and eliminated the interfering return loop radiation.

Images

FIGURE 10.28
Inserting different resistances in the LCR shown in Figure 10.27 changed the shapes of the LCR radiated field strength at the distance 90 cm from radiating antenna. (a) R = 1.2 Ω produces prominent near-field components even at distances of 90 cm. (b) Increased R = 3.2 Ω causes the near-field components to considerably diminish. (c) Increasing to R = 10.6 Ω they appear practically negligible.

The authors and their colleagues Lukin, and Kholod suggest another way to prevent undesirable radiation [13,17]. It consists of using a cylindrical shield as shown in Figure 10.31. The cylindrical metal shield divides the whole space into an external and internal part. If the return loop is within the cylinder along its axis, it localizes the energy of the pulse driver in the internal space and eliminates its effect on the radiated electromagnetic field strengths.

However, when the pulse reaches the junction to the radiating antenna, it induces a voltage between outer ends of the metallic shield. This voltage produces a current on the outside surface of the metallic shield. This outside surface current flows opposite to the current flowing through the radiator and the LCR works as a quadrupole rather than a dipole radiator.

Images

FIGURE 10.29
The amplitude of a short pulse forming the radiating signal at distance r for resistances R = 1.2, 3.3, and 10.6 Ω. Although the amplitudes show little difference, the waveform quality varies greatly from the high-near-field effects of R = 1.2 and R = 3.2 Ω when compared with R =10.6-Ω cases shown in Figure 10.28.

Images

FIGURE 10.30
The ratio of the signal amplitude U_1.2Ω/U_10.6 and U_3.2Ω/U_10.6 for antennas compared with R = 10.6-Ω antenna resistance. This shows the minor advantage of low-resistance antennas, which also have less pure pulses than R = 10.6-Ω case.

A layer of ferrite covering helps to suppress radiation from the outside surface of the metallic shield as shown in Figure 10.31. This reduces the electromagnetic wave radiated from the outside surface of the metallic shield owing to the absorption of energy by the ferrite when it becomes magnetized. Owing to large inductance of the outside surface of the metallic shield conditioned by the ferrite layer, the current rises and falls more slowly there. According to Equations 10.1 and 10.2, a small time derivative of the current implies small field strengths.

For more efficient absorption of the energy flowing along the surface of the metal shield, the return loop uses a shield by one metal and two ferrite layers: an internal layer made of low-frequency ferrite and an external layer of high-frequency ferrite. Experiments have shown that the combination of a metallic and a ferrite shield effectively suppresses the return loop radiation. It promotes dipole radiation of the LCR without a reduction of the amplitude of the current driven through the radiator. Pochanin and Kholod tested only a metal cylindrical shield in their work [14]. Figures 10.32 through 10.34 show how this shield had additional coatings of two layers of low-frequency and high-frequency ferrite [13,17].

The LCR return loop occupies a large space, so a more advanced design places the “traveling wave” pulse generator composed of seven sequence pulse generators with avalanche transistors inside the cylindrical metal shield [14]. This improvement permits removing the return loop that provided a dipole radiation mode and increased both the exciting signal amplitude and the radiated field amplitude, respectively, by more than 6 times (in comparison with a one-stage generator).

Images

FIGURE 10.31
The cross-section of the cylindrical shield suggested by Lukin, Pochanin, Masalov, and Kholod as a way to separate the antenna radiator from the return loop and improve radiation characteristics. (Pochanin, G.P. et al., “Large current radiator with S-diode switch,” IEEE Transactions on Electromagnetic Compatibility, 2001, 43, 1, 94-100, © 2001 IEEE.)

Images

FIGURE 10.32
The LCR with an avalanche transistor switch. (Lukin, K.A. et al., “Large current radiator with avalanche transistor switch,” IEEE Transactions on Electromagnetic Compatibility, 1997, 39, 2, 156-160, © 1997 IEEE.)

From the work of Pochanin, Kholod, and Masalov [17], the dipole radiation mode was demonstrated by measuring the dependencies of radiated field strength on radiation direction as shown in Figures 10.35 and 10.36 and the corresponding radiation patterns as shown in Figures 10.37 and 10.38.

Images

FIGURE 10.33
An LCR built with a traveling wave pulse generator. (Pochanin, G.P. and Kholod, P.V., “LCR with a traveling wave pulse generator,” The Third International Conference “Ultra Wideband and Ultra Short Impulse Signals,” September 18-22, 2006, Ukraine, © 2006 IEEE.)

Images

FIGURE 10.34
An LCR with an S-diode (avalanche effect) switch. (Pochanin, G.P. et al., “Large current radiator with S-diode switch,” IEEE Transactions on Electromagnetic Compatibility, 2001, 43, 1, 94-100, © 2001 IEEE.)

10.4.4 How to Reduce the Radiator Inductance

Because the radiating LCR antenna is a metal conductor, the amplitude and time characteristics of current pulses flowing in it depend on the radiator inductance. Large radiator inductance has to be reduced because of the following:

The large inductance prevents current buildup in the radiator. The transient time increases and dI_rad/dt decreases.
It is difficult to make an aperiodic current flow through the radiator if inductance is large and the resistance of the LCR is small.

Images

FIGURE 10.35
Dipole radiation measurements of the LCR combining a S-diode pulse generator built inside the cylindrical metal shield of Figure 10.34. This design eliminated the return loop and provided a dipole radiation mode. Plots show the angular dependence of the radiated waveform measured in the E-plane. (Pochanin, G.P. et al., “Large current radiator with S-diode switch,” IEEE Transactions on Electromagnetic Compatibility, 2001, 43, 1, 94-100, © 2001 IEEE.)

A large part of the energy of the pulse driving the radiator becomes stored in a local magnetic field strength and does not radiate to the far zone.
After the exciting generator switches a pulse into the LCR antenna, the antenna inductance and high rate of current change can create a high voltage, which can damage the semiconductors of the driving circuit.

Let us consider possible ways to decrease the inductance using a radio engineering technique. By connecting several wires in parallel we can decrease the inductance in comparison with inductance of a single wire. Building a radiating antenna from several conductors provides a solution.

Images

FIGURE 10.36
Angular dependence of the form of radiated signal in the H-plane of the LCR shown in Figure 10.35. (Pochanin, G.P. et al., “Large current radiator with S-diode switch,” IEEE Transactions on Electromagnetic Compatibility, 2001, 43, 1, 94-100, © 2001 IEEE.)

Increasing the radiating plate width provides another way to decrease the inductance. Simulation results by Pochanin, Masalov, and Kholod and by those researchers discussed in Section 10.4.1.1 demonstrate the growth of the radiated field strength at the increase of the radiating plate width [20,21]. This increased radiated field results from the current increase accompanying decreased antenna inductance.

A last way to decrease the inductance comes from additional radiator parts that shunt the EMF that appears as a result of a high rate of current entering the radiating antenna. For example, on placing a conductor with inductance L_w1, which is inductance of single wire, shown in Figure 10.39a, above a metal surface, as shown in Figure 10.39b, and applying a voltage pulse U_g(t) with a fast rise time to its ends, a current I_w moves in it. At that point, the EMF ψ_w1 from the conductor will excite, by displacement currents, the current I_p in the metal surface at a direction opposite to the current direction in the conductor. The metal surface quasi “shunts” a part of the EMF voltage, thereby reducing the EMF amplitude of the self-induction ψ_w1 in the conductor, as well as the inductance of this conductor L_w < L_w1 as shown in Figure 10.39b.

Images

FIGURE 10.37
The dipole radiation pattern of the antenna in Figure 10.34 with the S-diode generator built inside the cylindrical metal shield. The radial scale shows the normalized E-field. (Pochanin, G.P. et al., “Large current radiator with S-diode switch,” IEEE Transactions on Electromagnetic Compatibility, 2001, 43, 1, 94-100, © 2001 IEEE.)

Images

FIGURE 10.38
The H-plane radiation pattern of the antenna in Figure 10.34 with the S-diode generator built inside the cylindrical metal shield. The radial scale shows the normalized electric field. (Pochanin, G.P. et al., “Large current radiator with S-diode switch,” IEEE Transactions on Electromagnetic Compatibility, 2001, 43, 1, 94-100, © 2001 IEEE.)

Images

FIGURE 10.39
Inductance decreasing techniques. (a) A conductor with the inductance L_w1 (b) Placing the conductor above a metal surface, and applying the fast rise time voltage pulse U_g(t) to produce a current I_w. (c) Adding another conductor with current flowing in the opposite direction reduces the self-induction EMF ψ_w1 and ψ_w2, so the resulting inductance of each conductor becomes L_w1 = L_w2 < L_w. (Pochanin, G.P. and Masalov, S.A., “Use of the coupling between elements of the vertical antenna array of LCRs to gain radiation efficiency for UWB pulses,” IEEE Transactions on Antennas and Propagation, 2007, 55, 6, 1754-1759, © 2007 IEEE.)

By following this method, the inductance can be further decreased by placing an identical conductor, as shown in Figure 10.39c, close to the conductor through which a fast growing current with high amplitude must pass. In this additional conductor the same source will generate the current I_w2 by the drive pulse with the same parameters U_g(t), but the current direction should be opposite to the current direction in the first conductor I_w1. At that, the nearer we place both conductors to each other, the lower the self-induction EMF ψ_w1 and ψ_w2 becomes, so that the resulting inductance of each conductor L_w1 = L_w2 < L_w.

The following experimental LCRs took induction reduction into account during the design and development phases. Designs by Lukin, Kholod, and the authors used an approach based on widening the radiating plate [13,14,18]. The authors along with Kholod designed an LCR with the radiating element composed of five wide plates spaced at small distances from one another in order to reduce mutual induction [17].

Apart from unwanted radiation suppression, the metal cylindrical shield placed near the return loop helps to reduce the LCR inductance [13,17].

Extension of the cylindrical screen in the form of a transverse electromagnetic (TEM) horn antenna sections in the LCR with a traveling wave pulse generator and the LCR with S-diode switch resulted in (1) a two times amplified field pulse strength due to more essential decrease of the inductance; (2) an improvement of impedance matching of the radiator with the LCR driver; and (3) concentrating the direction of radiation by means of the horns [14,17].

Usually the process of forming powerful pulses for excitation of UWB antennas consists of two stages. The first stage accumulates and stores the energy necessary for the pulse. The second stage generates the pulse with a switching element that changes conductivity and produces a pulse with the desired rise and fall times and duration. Generally, a capacitor element accumulates the required energy to permit long-term pulse energy storage with small losses.

However, energy accumulation in an inductor provides another well-known design approach. As a rule, inductance storage requires large currents, for example, tens and even hundreds of amperes flowing through the inductance. The magnetic field around the inductor accumulates the energy. Quickly disconnecting the circuit produces a short pulse of high-voltage EMF at the terminals of inductance. The rise time and amplitude of the pulse depend on the rate of change of the circuit resistance and difference between its values before and after switching off the current. For example, the earliest experiments on energy transmission by Nicola Tesla and radio communication by Oliver Lodge used inductor-stored energy to form electromagnetic field pulses [24]. Modern scientific publications describe using this method of radiation for energy transmission [25] and for ground penetrating radar [26].

Naturally, inductive energy storage leads to considerable energy loss because of the small resistance in the circuit. Nevertheless, this way of pulse forming provides a desirable LCR excitation method. Because the inductance of the antenna prevents a fast current rise, exciting an LCR antenna by a pulse with fast rise time causes problems. At the same time, we can easily disconnect a circuit with large current in fractions of nanosecond. Equations 10.1 and 10.2 show that the efficiency of the LCR radiation does not depend on whether the current rises or falls, but it only depends on the rate of change of the current. Exciting an LCR based on disconnecting a large current looks like a promising way to increase performance. This has a special attraction because the inductive radiating element of LCR itself can store the energy for the pulse generator.

Figure 10.40 helps in understanding the peculiarities of LCR antenna excitation. At the onset, the switch S is closed and the applied voltage U₁ causes the current j₂ to flow through the radiator. Because the LCR radiator has inductance, it makes the current rise time quite long. When the current reaches its maximum (the maximum value depends on output impedance of the pulse source and could be very large), the switch is opened. If the switching time is 1 ns or less, the voltage U₂ across the switch S rises to very high amplitude, from the EMF induced by current when we interrupt it in the circuit with an inductance. This EMF produces pulse of electromagnetic field that propagates from the antenna.

So, the idea is to store energy around the loop in the form of a magnetic field for a long term (unlike the common case when the energy usually is stored in capacitance of a pulse generator), and to launch the energy in the form of short pulses of electromagnetic waves into free space by means of switching off the switch S.

To demonstrate the inductive LCR antenna, an antenna and appropriate exciter shown in Figure 10.41 were developed. The exciter applied an EMF of about 300 V with a rise time in the range of 0.15 to 0.5 ns (fixed value). The radiator had the following dimensions: 7 cm width, 3 cm height, and 9 cm length; the width included the printed circuit board. Several experiments evaluated the properties of the new LCR and compared the radiation efficiency in different excitation modes.

Images

FIGURE 10.40
The LCR antenna excitation principle. (a) The LCR and exciter form an LR circuit. (b) Closing the switch S applies voltage U₁ to drive the current j₂ through the radiator. (c) The antenna inductance makes the current rise time quite long. (d) When the current reaches its maximum, the switch S opens. (e) For short switching times, the EMF induced by current produces an electromagnetic field pulse that propagates from the antenna. (Pochanin, G.P. and Pochanina, I. Y., “Proper mode of excitation for large current radiators,” 5th International Conference on Ultrawideband and Ultrashort Impulse Signals, September 6-10, 2010, Sevastopol, Ukraine, © 2010 IEEE.)

Images

FIGURE 10.41
The inductive LCR test model with the exciter circuitry, which applied about 300-V EMF with a rise time in the range of 0.15 to 0.5 ns (fixed value). Dimensions: 7-cm width, 3-cm height, 9-cm length, the width included the printed circuit board. (Pochanin, G.P. and Pochanina, I. Y., “Proper mode of excitation for large current radiators,” 5th International Conference on Ultrawideband and Ultrashort Impulse Signals, September 6-10, 2010, Sevastopol, Ukraine, © 2010 IEEE.)

Mode 1 Test: In the first mode, the inductive storage described earlier was used by connecting the radiator to the secondary winding of the transformer. Applying a voltage pulse of U = 12 V from the pulse generator to the primary winding and closing the switch caused current to flow through the radiator. The current increased quite slowly; however, it reached an amplitude of up to 10 A. This rise time lasted for tens of nanoseconds. Then the switch S was turned off to produce a radiated pulse of the shape shown in Figure 10.42, Signal 1, at 50 cm distance from the LCR.

Mode 2 Test: In the second high-voltage mode, a zero current amplitude was maintained in the radiator before switching off. The LCR antenna shown in Figure 10.43 differs from the one shown in Figure 10.42 in the following manner. The switch S was removed from the ends of antenna arms to the ends of the secondary winding. Disconnecting the antenna arms prevented the current flow through the radiator before generating the driving pulse by closing S. The driving pulse was generated after interrupting current in the secondary winding. Signal 2 in Figure 10.43 shows the resulting radiated antenna signal.

Mode 3 Test: The third mode combined features of the large current mode and the highvoltage mode. The driving signal arises at the end of the secondary winding of the transformer. A resistor R = 240 Ω connects the radiator ends as shown in Figure 10.44. Closing the switch S produces the radiated Signal 3.

Mode 4 Test: The fourth mode shown in Figure 10.45 corresponds to the condition used in most antennas where a transmitter connects to a remote antenna. An independent pulse generator forms and delivers the driving signal to the radiator by a pair of 0.6-m long, 50-Ω coaxial cables. Taking into account that pulse propagates from the switch S to the radiator for 3 ns, it is reasonable to suppose that inductance of the radiator does not participate in generating the driving pulse. The antenna radiates Signal 4.

Images

FIGURE 10.42
Mode 1 radiator experiment used the inductive LCR test model of Figure 10.41, where a transformer powers the antenna-driving circuit. The radiated Signal 1 results from a 10 s of nanosecond pulse applied to a transformer primary. (Pochanin, G.P. and Pochanina, I. Y., “Proper mode of excitation for large current radiators,” 5th International Conference on Ultrawideband and Ultrashort Impulse Signals, September 6-10, 2010, Sevastopol, Ukraine, © 2010 IEEE.)

Images

FIGURE 10.43
Mode 2. This LCR antenna differs from the one in Figure 10.42 because the switch has moved from the ends of the antenna arms of the secondary winding. Disconnecting the antenna arms prevented the current flow through the radiator before generating the driving pulse by closing S. Interrupting the current in the secondary winding generates the driving pulse, which sends a current j₂ to the radiator. Closing S creates a driving pulse and produces the radiated Signal 2. (Pochanin, G.P. and Pochanina, I. Y., “Proper mode of excitation for large current radiators,” 5th International Conference on Ultrawideband and Ultrashort Impulse Signals, September 6-10, 2010, Sevastopol, Ukraine, © 2010 IEEE.)

Images

FIGURE 10.44
The Mode 3 LCR antenna combines features of the large current and high-voltage modes shown in Figures 10.42 and 10.43. This radiator design adds R = 240-Ω resistor between the radiator ends. Closing S produces the radiated Signal 3. (Pochanin, G.P. and Pochanina, I. Y., “Proper mode of excitation for large current radiators,” 5th International Conference on Ultrawideband and Ultrashort Impulse Signals, September 6-10, 2010, Sevastopol, Ukraine, © 2010 IEEE.)

Images

FIGURE 10.45
The Mode 4 LCR antenna duplicated the conventional case of a transmitter connected to a remote antenna. This test used an independent pulse generator and 0.6-m 50-Ω coaxial feeds to the radiating elements and produced Signal 4. The coaxial cables put a 4-ns delay from the time of pulse generation until transmission. (Pochanin, G.P. and Pochanina, I. Y., “Proper mode of excitation for large current radiators,” 5th International Conference on Ultrawideband and Ultrashort Impulse Signals, September 6-10, 2010, Sevastopol, Ukraine, © 2010 IEEE.)

A comparison of the experiments of Modes 1 to 4 in changing the LCR configuration demonstrated the following:

The large current Mode 1 is the most effective, because the largest amplitude of radiated field is generated in this mode.
The large current Mode 1 produces the shortest pulses in the form of the first derivative of the Gaussian pulse.
All signals show late-time ringing, but the Mode 1 large current has the lowest ringing level.

10.4.5 Design of Multielement LCR Radiators

Applying the lessons of the previous sections helps to design an LCR and exciting circuit that

Has a generator that can excite large current pulses with a preset duration and rise time in the radiator.
Has an optimum size radiating antenna that permits effective radiation of the energy in the form of a short electromagnetic pulse and without late-time ringing.
Has a reduced inductance to increase the radiated field strength.
Has properly designed shield parameters to suppress radiation of the return loop.

By achieving these objectives, we can further increase power of the radiated pulse by means of increasing the number of radiating antennas and summing the field strengths from all of the radiating antennas. This approach leads to creation of an antenna array.

In the case of conventional antenna arrays, there is little coupling between the antennas. The LCR antennas investigated here have considerable coupling due their close spacing. Therefore, they are rather multielement antennas than antenna arrays.

Figure 10.46 shows the LCR design for four pulse generators [18]. Figure 10.47 shows an LCR excited by octa-output 25-Ω buffers/drivers with 3-state outputs using SN74BCT25244-D shown in Figure 10.13, which increases the radiated signal amplitude.

The close relative position of the radiators shown in Figures 10.46 and 10.47 leads to strong coupling between them, caused by their mutual inductance. Big problems arise when pulse generators operating in the switch mode excite the radiators. In this case, the parameters of a pulse formed by switches (first of all, pulse start time and amplitude) depend greatly on the operating conditions of the switching element. As a result, the pulse start time changes with the electrode voltage.

Since real switching elements have some performance spread, one element will switch on before all the others. Because of the strong coupling of radiating elements, the EMF induced in neighbor elements will appear in the electrodes of corresponding switches. This mutual coupling will cause the time shifts of the exciting signals in neighboring radiators. This leads to the breakdown of radiation synchronization and decreased radiated field strength when compared to the expected strength if all elements radiated simultaneously.

Images

FIGURE 10.46
The LCR multielement array with silicon FET switches and four radiating antennas. (Adapted from Pochanin, G.P., “Radiation of pulse signals of variable duration by tunable large current radiator,” Radiofizika i elektronika, 5, 2, 118-127, 2000.)

Images

FIGURE 10.47
A multielement LCR antenna with a microcircuit switch and 16 radiating antennas. The assembly has octa-output 25-Ω buffers/drivers with 3-state outputs using the SN74BCT25244-D circuits shown in Figure 10.13 to increase the radiated signal amplitude.

The author’s experiments with the tunable LCR of Figure 10.46 in the switch mode showed that when all four switches were turned on simultaneously, an unstable operating mode was produced [18]. However if all the switches were turned on simultaneously, the radiated field amplitude became approximately 1.8 times higher than the field amplitude in other experiments.

The next series of experiments demonstrated how mutual coupling between the antenna elements could strongly impede attempts to increase the radiation efficiency. The LCR design shown in Figure 10.47 included 16 elements excited by microcircuit switches. The testing determined the radiation efficiency that could result from consecutively increasing the number of radiating elements connected to generators. Experimental results showed that connecting the second element increased the field amplitude by 1.8 times. Connecting the third element caused the amplitude to increase by 2.2 times. Adding more elements only slightly influenced the far-field amplitude. However, the antenna power consumption increased in proportion to the number of radiators engaged without any increase in radiated power.

Thus, it can be concluded that strong coupling between antenna elements prevents increasing the radiation efficiency of multielement antennas.

However, it appears that these results only apply to the multielement LCR with radiating antennas so that the magnetic fields generated in every antenna at excitation by a current pulse are co-directional. Figure 10.48a shows this condition where the induced currents in neighboring antennas oppose the driving currents. Therefore, in every radiating antenna the summed current, composed of the driving current and the current induced by the neighboring element, is smaller than the driving current by the value of the induced current.

Images

FIGURE 10.48
Variants of positioning of radiating antennas of the multielement LCR. (a) The case where adjacent elements induce currents in the opposite direction to the driving currents. (b) The Harmuth solution of placing the elements to induce currents in the same direction as the driving currents. (c) The experimental four-element LCR using GaAs switching technology and adjacent element co-directional current induction produced a radiated field 6X the field of one radiating element. (Pochanin, G.P. and Masalov, S.A., “Use of the coupling between elements of the vertical antenna array of LCRs to gain radiation efficiency for UWB pulses,” IEEE Transactions on Antennas and Propagation, 2007, 55, 6, 1754-1759, © 2007 IEEE.)

To prevent the interference of the strong electromagnetic coupling between radiating antennas and to provide an increase of the LCR radiation efficiency, Prof. H.F. Harmuth suggested placing the loops of the radiating antennas in a single plane as shown in Figure 10.48b. In this arrangement, the magnetic field, excited by loop 1, induces the current in loop 2 that has the same direction with the current induced in loop 2 by exciter driving signal. This produces a larger current amplitude in the radiating antenna than the current that rises during excitation without the neighboring radiating antenna. This effectively lowers the LCR inductance and increases the radiation effectiveness.

Both the theoretical estimate and experimental data demonstrate the assumptions by Prof. H.F. Harmuth to increase the LCR radiation efficiency. The experiments were performed by the author on the four-element LCR shown in Figure 10.48c. This four-element LCR used excitation by four switches with the GaAs FET described in Section 10.3.5. Experimental results demonstrated that this four-element LCR radiates a field strength at least 6 times as large as the field strength of one array element [27]. Figure 10.49 compares (1) the single radiator and (2) multiple radiator pulses from the four-element LCR array. This provides more than the sum of the field strengths of the single elements.

Thus, in spite of the considerable electromagnetic coupling between radiating elements prevents the effective radiation of pulsed electromagnetic fields by multielement antennas as shown in Figures 10.46 and 10.47, by using the Harmuth solution of placing elements to induce co-directional currents as shown in Figure 10.48c, the achievable radiation efficiency of the LCR can be not only proportional to number of elements but can also be substantially greater.

10.4.6 How to Control the LCR Radiated Pulse Duration

Experimental results have shown how the multielement LCR with silicon FET switches shown in Figure 10.46 can radiate pulses of different durations by changing the current rate in the radiator [18]. The excitation circuits, the exciting currents, and antenna array shown in Figures 10.9 through 10.11 work in a linear amplification mode allowing the control of the pulse time duration.

Images

FIGURE 10.49
Experimental results for the antenna shown in Figure 10.49c. Measured radiation pulse field from (a) the small LCR (an element of the array) and received at a distance of 50 cm from the antenna; and (b) the four-element vertical array of LCRs and received at a distance of 1 m from the antenna. This four-element array antenna used the Harmuth co-directional induced current concept to improve performance. (Pochanin, G.P. and Masalov, S.A., “Use of the coupling between elements of the vertical antenna array of LCRs to gain radiation efficiency for UWB pulses,” IEEE Transactions on Antennas and Propagation, 2007, 55, 6, 1754-1759, © 2007 IEEE.)

Figure 10.50 shows the results of measurement of the angular dependence of the radiated pulse form of the electromagnetic field in the plane E at a distance of 1.8 m from the multielement silicon FET LCR shown in Figure 10.46. Dotted lines and solid lines show field pulses radiated by LCR at excitation of radiating elements by pulse signals with a rise time of 5 ns and 3 ns, respectively.

For the multielement FET LCR, the first pulses with negative polarity have durations corresponding to the drive signal rise time. The exception occurs at directions 90°−120° and 240°−270°, for which the first pulse durations are practically equal. A large positive pulse going into the oscillatory process with the period of the order of 10 ns follows the first pulse of negative polarity. The plots corresponding to directions 90°−120° and 240°−270° show oscillations. The plots also show pulses that have come in the receiver after reflecting from the laboratory floor and walls, as well as oscillations caused by re-reflections in the receiver feeder lines and in the cables feeding the multielement FET LCR. A small overshoot at the top of the drive signal causes the presence of the first positive pulse. Reducing the power amplifier gain suppressed this overshoot. This case was tested and demonstrated, but this reduced the radiated field strength.

During measurements, the value of resistance R_d in the radiating element circuit remained permanent. Thus, the amplitude of the driving current pulse I_rad did not change. Therefore, according to Equations 10.1 and 10.2, the amplitudes of the field pulse radiated in the far zone from excitation by a pulse with the front duration Δt = 5 ns appears to be nearly a half of the amplitude of the field pulse radiated in the far zone at excitation by a pulse with the rise time Δt = 3 ns. By appropriately reducing the value of damping resistance R_d, these amplitudes will equalize.

Images

FIGURE 10.50
Experimental results from the multielement silicon FET LCR of Figure 10.46. The plot shows how the signal waveform depends on the angle of measurement and the exciting pulse duration. As would be expected, the sideways (90° and 270°) waveforms show a decrease from the spatial displacement of the radiating elements. (Adapted from Pochanin, G.P., “Radiation of pulse signals of variable duration by tunable large current radiator,” Radiofizika i elektronika, 5, 2, 118-127, 2000.)

By increasing the rise time of the driving current pulse Δt from Δt_min to Δt_max and accordingly by proportionally reducing the value R_d from R_{d max} to R_{d min}, it is possible to receive a proportional increase of ΔI_rad from ΔI_{rad min} to ΔI_{rad max}. Here the values of strengths of the radiated field Equations 10.1 and 10.2 will be constant for different durations of Δt from Δt_min to Δt_max. In practice, this possibility requires using an electrically controlled resistor.

Thus, the experiments show that the LCR radiated pulse duration can be controlled.

10.5 Conclusion

Until now, our specific interest in the LCR came as a way to study the fundamental properties of transient electromagnetic fields and processes related to their radiation. The results of the experiments carried out with various forms of LCR demonstrated the principles and peculiarities of electromagnetic field radiation from large currents.

At present, the LCR has limited applications. As we have shown, the structure and electrical properties of the LCR such as high inductance and electromagnetic coupling between elements present considerable challenges to the antenna engineer.

The investigation of the physical principles of radiating transient pulse electromagnetic fields by LCRs has just started. However, the variety of properties discovered during experimental investigations and theoretical analysis of different LCR designs holds out a hope of developing new effective, economic, and user-friendly radiators, which are based on the principle of operation of Harmuth’s LCRs.

10.6 Acknowledgments

The authors express their gratitude to Prof. Henning F. Harmuth for the breakthrough ideas he has given in his now classic books and articles. Many of his ideas have found acceptance as axioms in the nonsinusoidal electrodynamics area. Considering the results he achieved, more than one generation of scientists will learn and build their achievements on the basics he developed. Very few scientists have discovered something really new and important, and an even lesser number can confirm their opinions and openly fight for them. The authors contacts with Prof. H.F. Harmuth provided much useful advice, helpful criticisms, valuable help, and support.

The authors are indebted to Alan E. Schutz (Geophysical Survey Systems, Inc., USA) and Dr. Robert A. Fleming (AetherWire & Location, Inc USA) for supporting these investigations and thank Dr. Pavlo V. Kholod (IRE NAS of Ukraine) for his contribution to the experimental investigation.

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27. Pochanin G.P. and Masalov S.A. 2007. Use of the coupling between elements of the vertical antenna array of LCRs to gain radiation efficiency for UWB pulses. IEEE Transactions on Antennas and Propagation, Vol. 55, No. 6, pp 1754-11759.

28. Pochanin G.P., and Pochanina I.Ye. Proper mode of excitation for large current radiators. 5^th International Conference “Ultrawideband and Ultrashort Impulse Signals,” September 6-10, 2010, Sevastopol, Ukraine.

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Table of Contents for 10 Large Current Radiators: Problems, Analysis, and Design

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Table of Contents for
10 Large Current Radiators: Problems, Analysis, and Design